Questions

  1. How do species differ in their drought response to variable intensity and their recovery patterns?
  2. If species differ, do they also vary regionally? For which species?
  3. Are drought response and recovery mediated by competition and tree size and is this a species specific phenomenon or does it also vary regionally?

Methods

I collected tree ring data from 4 regions across California and performed analyses on detrended growth during drought years where water availability (SPEI) was in the bottom 10th percentile. All tree ring series were spline detrended.

Key responses

\[ Growth Reduction = \frac{\overline{RWI}_{non-drought} - RWI_{drought}}{\overline{RWI}_{non-drought}} \] \[ Recovery = RWI_{actual} - RWI_{pred} \]

Where \(RWI_{pred}\) is the predicted growth for a tree given the post-drought year conditions based on hierarchical Bayesian models of all growth years.

Full model approach to Q3

This approach differs in that here we explore the results of the full expression of the model to answer the above questions i.e. the most complex justifiable model. Each species is modeled independently. This approach is a way to avoid the model selection issues we discussed regarding the complexity of question 3.

\[ Reduction_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}SPEI_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}SPEI_i\times DBH_i + \beta_{5}SPEI_i \times BA_i \]

and for recovery:

\[ Recovery_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}Reduction_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}Reduction_i\times DBH_i + \beta_{5}Reduction_i \times BA_i \]

Regionally varying responses to drought intensity or severity could reflect local adaptation.

Descriptions of interaction terms

\(SPEI \times DBH\) smaller or larger trees experience the same drought intensity differently. Perhaps this is due to differences in evaporative demand, root:shoot allocation patterns, height water relationship

\(Reduction \times DBH\) smaller or larger trees recover from equally damaging droughts differently. Potentially due to access to resources, allocation again.

\(SPEI \times BA\) sparse or dense neighborhoods modify the effect of drought intensity. This could be via resource (water) competition. Although because we lack good characterization of the between neighborhood microsite differences density could reflect suitability more than competition.

\(Reduction \times BA\) sparse or dense neighborhoods modify the recovery of trees from equally damaging droughts. This could also be via resource competition although more than just water. Again, patterns may reflect uncharacterized microsite differences rather than competition.

Details

All models converged Rhat ~1 and each model had few divergent samples. Param estimates and plots were prepared with tidybayes. Marginal effects plots were produced with add_fitted_draws() .

Results

Q1 Species differences

Growth Reduction

Table SX. Growth reduction WAIC table
waic_diff se
SPEI only 0.00000 0.000000
Species + SPEI 2.04252 3.076878
Species * SPEI 4.74648 3.720620
Table SX. Growth reduction variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0666103 0.0096405 0.0505275 0.0820601 Inf 1.0000
PL - AC > 0 0.0342796 0.0118112 0.0155830 0.0540833 9.9900e+02 0.9990
PL - PJ > 0 -0.1272120 0.0475280 -0.2065795 -0.0489364 5.5304e-03 0.0055
Table SX. Growth reduction intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0205816 0.0136596 -0.0024442 0.0429330 14.094340 0.93375
PL - AC > 0 0.0103469 0.0157787 -0.0155560 0.0364456 2.906250 0.74400
PL - PJ > 0 -0.0102347 0.0161652 -0.0368797 0.0164271 0.356392 0.26275

Recovery

Table SX. Recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.00000
Varying intercept 4.186948 10.25373
No species effect 12.834264 12.04065
Table SX. Recovery variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0551883 0.0086157 0.0409969 0.0693746 Inf 1.00000
PL - AC > 0 0.0358049 0.0107017 0.0183191 0.0538784 3.99900e+03 0.99975
PL - PJ > 0 -0.0891320 0.0502752 -0.1715589 -0.0051960 4.32968e-02 0.04150
Table SX. Recovery intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0315932 0.0175444 0.0029861 0.0603802 27.98551 0.96550
PL - AC > 0 0.0967908 0.0224670 0.0598268 0.1338717 Inf 1.00000
PL - PJ > 0 0.0651976 0.0225358 0.0287279 0.1016507 1332.33333 0.99925
Table SX. Recovery slope contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 -0.0809188 0.0411304 -0.1481597 -0.0133473 0.025641 0.02500
PL - AC > 0 0.0800334 0.0534826 -0.0074203 0.1685892 14.094340 0.93375
PL - PJ > 0 0.1609522 0.0511764 0.0771802 0.2447245 1332.333333 0.99925

Param Plots

Main Figure

Q2 Regional Differences

Growth Reduction

Table SX. A. concolor growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
No regional effects 43.30953 12.80732
Varying intercept 45.11601 12.72891
Table SX. P. jeffreyi growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
Varying intercept 41.83552 12.88420
No regional effects 43.82051 13.91644
Table SX. P. lambertiana growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.000000
No regional effects 18.41681 7.836080
Varying intercept 19.29546 7.449942
Table SX. ICC for regionally varying parameters (AC, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.5970135 0.1336668 0.3013006 0.8868626 NA NA
region slope/total 0.2677814 0.1137323 0.0737678 0.5785439 NA NA
Table SX. ICC for regionally varying parameters (PJ, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.5486569 0.1608815 0.2163339 0.8879885 NA NA
region slope/total 0.2554130 0.1337445 0.0574560 0.6456691 NA NA
Table SX. ICC for regionally varying parameters (PL, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.4047434 0.3123458 0.0035201 0.9735754 NA NA
region slope/total 0.4766134 0.3515581 0.0141206 0.9946826 NA NA

Recovery

Table SX. A. concolor recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 1.851447 5.964911
No regional effects 12.912958 9.351119
Table SX. P. jeffreyi recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 7.988191 8.352711
No regional effects 22.441717 12.987328
Table SX. P. lambertiana recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 4.836886 8.154183
No regional effects 36.244175 11.872226
Table SX. ICC for regionally varying parameters (AC, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.2333188 0.2132561 0.0152736 0.8137307 NA NA
region slope/total 0.3221096 0.2583555 0.0039577 0.8943126 NA NA
Table SX. ICC for regionally varying parameters (PJ, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.1958702 0.2089063 0.0081197 0.8032205 NA NA
region slope/total 0.3258525 0.2541065 0.0158146 0.9298125 NA NA
Table SX. ICC for regionally varying parameters (PL, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.2531975 0.2850897 0.0014873 0.9548398 NA NA
region slope/total 0.5320250 0.3267092 0.0123234 0.9933452 NA NA

Param Plots

Main Figure

Q3

Param Plots

Main Figure

Growth Reduction

Keep in mind that in the scatter plots the drought intensity axis is flipped, so slope will appear to be wrong sign from the parameter estimate plots.

Recovery